Summary
An integral inequality for the eigenfunctions of linear second order elliptic operators in divergence form is proved. The result is a generalization of the Payner-Rayner inequality.
Résumé
On démontre une inégalité intégrale pour les fonctions propres d'une classe d'opérateurs linéaires élliptiques du deuxième ordre. Le résultat est une généralization de l'inégalité de Payner-Rayner.
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References
G. Chiti,Norme di Orlicz delle soluzioni di una classe di equazioni ellittiche. Boll. Un. Mat. Ital. (5) 16-A (1979).
G. Chiti,An isoperimetric inequality for the eigenfunctions of linear second order elliptic operators (To appear on Boll. Un. Mat. Ital.).
G. H. Hardy, J. E. Littlewood, and G. Polya,Some simple inequalities satisfied by convex functions. Messenger Math. 58 (1929).
M. T. Kohler-Jobin,Sur la première fonction propre d'une membrane: une extension à N-dimensions de l'inegalité isopérimétrique de Payne-Rayner. Z. Angew. Math. Phys.28, 1137–1140 (1977).
L. E. Payne and M. E. Rayner,An isoperimetric inequality for the first eigenfunction in the fixed membrane problem. Z. Angew. Math. Phys.23, 13–15 (1972).
L. E. Payne and M. E. Rayner,Some isoperimetric norm bounds for solutions of the Helmholtz equation. Z. Angew. Math. Phys.24, 105–110 (1973).
G. Talenti,Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa (4) 3 (1976).
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This study was performed within the G.N.A.F.A. of the Italian C.N.R.
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Chiti, G. A reverse Hölder inequality for the eigenfunctions of linear second order elliptic operators. Z. angew. Math. Phys. 33, 143–148 (1982). https://doi.org/10.1007/BF00948319
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DOI: https://doi.org/10.1007/BF00948319